Meta Optimality for Demographic Parity Constrained Regression via Post-Processing

We address the regression problem under the constraint of demographic parity, a commonly used fairness definition. Recent studies have revealed fair minimax optimal regression algorithms, the most accurate algorithms that adhere to the fairness constraint. However, these analyses are tightly coupled with specific data generation models. In this paper, we provide meta-theorems that can be applied to various situations to validate the fair minimax optimality of the corresponding regression algorithms. Furthermore, we demonstrate that fair minimax optimal regression can be achieved through post-processing methods, allowing researchers and practitioners to focus on improving conventional regression techniques, which can then be efficiently adapted for fair regression.

Machine learning systems are increasingly used to make important decisions in areas like healthcare, finance, and criminal justice. However, these systems can sometimes treat different groups of people unfairly - for example, showing bias against certain racial groups, genders, or age groups. While researchers have developed methods to make these systems fair, the theoretical understanding of when these methods work best has been limited to specific situations.We developed a new theoretical framework that helps us understand when and how to make machine learning systems fair across a wide range of situations. Our analysis shows that a common approach called post-processing - where we first build a prediction system and then adjust its outputs to ensure fair treatment - can be theoretically proven to be the best possible approach in many more scenarios than previously thought. We also provide guidance on how to construct these post-processing methods to achieve the best possible performance.Our work provides a theoretical foundation that helps practitioners choose and implement the best fairness methods for their specific applications. This is particularly important as machine learning systems become more widespread in society, where unfair treatment can have serious consequences for individuals and communities. Our findings give practitioners more confidence in using established fairness techniques across different applications.